Efficient Simulation of Freak Waves in Random Oceanic Sea States

Numerical simulations of freak wave generation are studied in random oceanic sea states described by JONSWAP spectrum. The evolution of initial random wave trains is namerically carried out within the framework of the modified fourorder nonlinear Schroedinger equation （mNLSE）, and some involved influence factors are also discussed. Results show that if the sideband instability is satisfied, a random wave train may evolve into a freak wave train, and simultaneously the setting of the Phillips paranleter and enhancement coefficient of JONSWAP spectrum and initial random phases is very important for the formation of freak waves. The way to increase the generation efficiency of freak waves thsough changing the involved parameters is also presented.

Modulation instability analysis, optical and other solutions to the modified nonlinear Schr?dinger equation

This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrodinger equation,which models the propagation of rogue waves in ocean engineering.The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions.It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters.This method is beneficial for solving nonlinear partial differential equations,because it is not only useful for finding the new exact traveling wave solutions,but also gives us the solutions obtained previously by the usage of other techniques(Riccati equation,or first-kind elliptic equation,or the generalized Riccati equation as mapping equation,or auxiliary ordinary differential equation method)in a combined approach.Moreover,by means of the concept of linear stability,we prove that the governing model is stable.3 D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions.